Research On Decision Making Methods And Clustering Algorithms Under Hesitant Fuzzy Environments

With the development of modern economy and society, the fuzziness and uncertainty of the decision making problems that people consider have been enhanced significantly. Hesitant fuzzy sets (HFSs), which were proposed by Torra and Narukawa in 2010, are a powerful tool of handling the fuzziness encountered in decision making and clustering issues. The new concept allows the membership degree of an element to a set represented by several possible values. Therefore, HFSs provide a suitable manner to express hesitancy when decision makers give their evaluation values for alternatives. This paper focuses on the study of decision making methods and clustering algorithms under hesitant fuzzy environments. The main results obtained in our work are as follows:(1) The HFSs are extended to interval-valued hesitant fuzzy sets (IVHFSs). We define the concepts of IVHFS and interval-valued hesitant fuzzy element, explore the corresponding properties of mathematical operations and present relevant aggregation operators and distance measures. We establish interval-valued hesitant fuzzy preference relations, based on which we propose the decision making methods for the cases where the weights of the decision makers are known and unknown, which can intuitively address the difference in evaluation information given by the decision makers.(2) The hesitant fuzzy multi-attribute decision making methods based on the ELECTREs (ELimination Et Choix Traduisant la Realite) are proposed, and thus, the application domain of the ELECTREs is extended. We define the concept of deviation function and combine it with score function to give comparison laws for hesitant fuzzy elements (HFEs). We formulate outranking relations among alternatives using the concepts of concordance and discordance under hesitant fuzzy environments, and develop the hesitant fuzzy decision making methods based on ELECTRE I and ELECTRE II respectively.(3) The hesitant fuzzy multi-attribute decision making methods based on the assignment models are given. By means of the comparison laws for HFEs, we formulate a weighted preference ranking frequency matrix that accounts for the weights of attributes, and propose the hesitant fuzzy and interval-valued hesitant fuzzy decision making methods using the assignment models, which can give a total order of alternatives. In addition, we develop the assignment models based on HFEs and interval-valued hesitant fuzzy elements (IVHFEs), and give the corresponding methods to solve the developed models.(4) The algorithms are given for clustering hesitant fuzzy information. We establish the correlation coefficient formula and the correlation matrix for HFSs and IVHFSs, and give the hesitant fuzzy clustering algorithms using equivalent hesitant fuzzy correlation matrix. In addition, on the basis of the aggregation operators and distance measures for hesitant fuzzy information, we propose the hierarchical hesitant fuzzy K-means algorithm by combining both the hierarchical clustering algorithm and the K-means clustering algorithm.